Timely and Non-Disruptive Response of Emergency Vehicles: AReal-Time Approach

Pratham Oza

prathamo@vt.edu

Virginia Tech

Thidapat Chantem

tchantem@vt.edu

Virginia Tech

ABSTRACTFacilitating timely traversal of emergency response vehicles (ERVs),

especially through an urban road network remains a challenging

task. ERV preemption is a technique commonly used to facilitate

prioritized ERV traversal. Unplanned deployment of ERV preemp-

tion can induce network-wide traffic delays. This paper presents

an ERV preemption strategy (considering ERV urgency levels) that

proactively manages the traffic before, during and after ERV traver-

sal by leveraging connected infrastructure to guarantee timely ERV

travel while minimizing traffic delays. We also provide worst-case

wait time bounds for non-emergency vehicles during ERV preemp-

tion. Our proposed approach does not introduce any additional

delay in ERV traversal over existing approaches while also showing

up to 43% reduction in average non-emergency traffic delays.

ACM Reference Format:Pratham Oza and Thidapat Chantem. 2021. Timely and Non-Disruptive

Response of Emergency Vehicles: A Real-Time Approach. In 29th Interna-tional Conference on Real-Time Networks and Systems (RTNS’2021), April7–9, 2021, NANTES, France. ACM, New York, NY, USA, 12 pages. https:

//doi.org/10.1145/3453417.3453434

1 INTRODUCTIONWith 70% of the world’s population expected to live in major urban

cities by 2050 [4], traffic congestion continues to be one of the most

pressing issues of urbanization. Most urban cities across the globe

have observed a 46–71% increase in traffic congestion [34]. Limited

space for urban expansion, especially for existing roadways creates

a bottleneck in meeting increasing traffic demands, due to which

efficient traffic management has become of prime importance.

Congested roadways not only lead to increased commute times,

fuel consumption and pollution, but also hamper timely deployment

of emergency response systems [3]. With over 240 million 911 calls

being made every year just in the US alone [1], emergency response

vehicles (ERVs) often fail to meet their target response time due

to congested roads and thereby affecting the hospitalization and

mortality rates [15]. Congestion further lead to queue spillbacks

This work was supported in part by the National Science Foundation under grant

numbers CPS-1658225 and CPS-2038726. We would like to thank the reviewers and

the shepherd for their suggestions that helped in improving the manuscript.

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ACM ISBN 978-1-4503-9001-9/21/04. . . $15.00

https://doi.org/10.1145/3453417.3453434

and collisions disrupting the entire road network. Queue spillbacks

occur when there is a queue downstream of an intersection that

disrupts the discharge of vehicles even when the light is green,

thereby propagating the congestion and causing a gridlock [27].

As a common practice, the non-emergency vehicle (non-ERV)

drivers are required to pull over to the edge of the roadway, when

an ERV is approaching, to allow its safe traversal [32] through

congested roads. However, in dense urban areas, the edges of the

roadways are often occupied by moving traffic or parked vehicles,

leading to confusion among the drivers when the ERV approaches.

In such situations, it is not only infeasible to clear the traffic for the

ERV but potentially dangerous, causing the non-ERVs and ERVs

to collide. The chances of an ERV getting into a crash are even

higher when it enters an intersection block with cross-traffic move-

ments [12]. Such situations make it difficult for the ERVs to quickly

and safely traverse through the road network and meet their re-

sponse times. Collisions further exacerbate the network-wide traffic

flow, making it difficult to restore smooth operations. Thus, the

traffic lights at an intersection must detect and facilitate safe ERV

traversal, known as ERV preemption, while reducing the traffic de-

lays for non-ERV movements caused by the preemption.

In most existing ERV preemption techniques, the intersections

independently control the traffic lights upon detecting an ERV [38].

However, failure to detect an ERV especially in heavy traffic, ham-

pers the ERV’s travel. The network-wide ERV preemption approaches

[5] switch multiple traffic lights to green when an ERV arrival is

expected while turning the lights for cross-traffic movements to red.

Such techniques facilitate ERV traversal, but fail to minimize its

impact on non-ERV traffic leading to propagated spillbacks, which

may in-turn worsen the traversal time of other imminent ERVs [6].

Existing work either provide ERV preemption mechanisms with-

out reducing its impact on the non-ERVs [21] or optimize traffic

flows through a network without facilitating ERVs [26]. However,

by leveraging the connected infrastructure, ERV arrival information

can be acquired well in time to not only facilitate smoother and safer

ERV traversal but also reduce the queues in the cross-traffic move-

ments such that the delays after ERV preemption are minimized.

By translating a typical traffic network with both, non-emergency

and emergency vehicles into a real-time task scheduling problem,

we present an end-to-end ERV preemption technique that enables

safe and quick ERV traversal. Using a deadline-driven approach,

we also optimally control the network-wide traffic before, duringand after the ERV traversal to minimize queues and reduce traffic

delays. We highlight the following contributions of this paper:

• We provide an ERV preemption strategy that provides a safe

and timely ERV passage through a road network of multiple

intersections while optimally managing non-emergency traffic.

1

RTNS’2021, April 7–9, 2021, NANTES, France Oza et al.

• By leveraging real-time ERV arrival and traffic data, our approach

optimally manages the network-wide traffic before the ERV ar-

rives and after the ERV safely traverses, such that guaranteed

timely ERV response is accompanied with reduced queues.

• By using the triage scale [9] (Table 2), we propose a priority-based

deadline-driven ERV preemption mechanism.

• We provide worst-case performance analysis for the non-ERV in

presence of an ERV to enhance the predictability of emergency

dispatch and traffic management systems.

• We analyze the adaptability of our approach using large-scale

simulations and hardware-in-loop (HIL) testbed with robots that

mimic human-driven vehicles through urban environment.

2 RELATEDWORKThe majority of the incidents involving ERVs occur due to collisions

within the intersection [6]. Traffic lights in the US are therefore

equipped with detectors, such as the 3M Opticom™ [28] using

infrared and GPS communication, or IoT-based approaches with

multiple sensors [18]. Such approaches are not only vulnerable to

interference, but also lead to longer queues at the intersections

downstream in urban areas due to the lack of coordination [19].

ERV traversal through a network of intersections is enabled

by green wave coordination [16] where consecutive traffic lights

along the ERV’s path are turned green after a constant offset-based

time delay or a fuzzy decision-making process [5]. However, such

heuristic mechanisms, lead to prolonged red lights for the conflict-

ing flows causing long wait-times and possible spillbacks [17]. We

discuss in our evaluation (Section 6) that our approach improves

the ERV travel time as compared to the existing work, while also

reducing the network-wide non-ERV traffic delays.

ERV preemptionwith connected and autonomous vehicles (CAVs)

present in the traffic is studied in [13, 36] that utilize vehicle-to-

everything (V2X) and cloud connectivity to gather real-time traffic

information and control each vehicle for ERV preemption. The pres-

ence of 100% CAVs on road however, is not expected until 2050 [10].

While we leverage basic connectivity between intersections within

our road network to disseminate ERV information, our approach is

applicable for conventional, mixed and autonomous traffic.

Conversely, the existing traffic approaches that optimize traffic

for a road network do not consider ERV preemption [20]. The exist-

ing work [25, 26] proposed a task model to represent traffic through

an intersection or a network of intersections. Specifically, in [26],

a recovery mechanism to counter unexpected traffic disruptions

using optimal strategies was provided. However, facilitating ERV

movements through the road network was not addressed. In this

paper, we leverage the real-time task model for a road network to

provide timeliness and safety guarantees for ERV traversal while

ensuring predictable traffic flow through the network.

The available ERV preemption mechanisms are heuristic and fail

to minimize the ERV’s impact on network-wide traffic and vice-

versa. The existing traffic control strategies minimize travel time

through the road network but they do not allow ERV preemption.

In our work, we propose an end-to-end solution that utilizes real-

time traffic and ERV arrival information to a) ensure timely ERV

traversal, b) proactively organize traffic before ERV arrival to reduce

traffic delays, and c) clear congestion after ERV traversal.

3 SYSTEM MODELA real-time task model to represent traffic flows through a road

network was proposed in [26]. In this paper we extend the task

model to accommodate for prioritized ERV traversals.

3.1 Road Network and Traffic LightsFor our model, we use a Manhattan grid-like𝑚 × 𝑛 road network

formed by𝑚 and𝑛 arterials travelling along the east-west and north-

south direction, respectively. Therefore, there are𝑚𝑛 intersections

in our road network. Such a network can either be standalone or

a part of a larger urban area. An intersection is formed by four

arterials, each traveling in a different direction, where the traffic

flow within each arterial is controlled by a traffic light. Each arterial

passes through multiple intersections across the network forming

links that connect two consecutive intersections. For example, in a

3 × 3 network, there are nine intersections formed by three arteri-

als traveling along the north-south and east-west directions each

(Figure 1). The traffic moving along the north and the south (or

the east and the west) direction within each arterial can enter the

intersections at once without interfering with one another and are

therefore called non-conflicting pairs of directions. However, the

vehicles traveling along the east-west direction conflict the vehicleflow along the north-south direction, and vice-versa, and cannot

access the intersections simultaneously. We use the following nota-

tions to throughout the paper to identify the links, arterials, and

intersections within the network:

• D,Dc: directions of traffic flow, where 𝐷 ∈ {𝑁, 𝐸,𝑊 , 𝑆} (car-dinal directions) and complementary, non-conflicting pairs of

directions, where 𝐷𝑐 ∈ {𝑆𝑁, 𝐸𝑊 }, respectively.• m, n: number of arterials in east-west and north-south directions,

respectively.

• 𝜶, 𝜶𝒓 : dummy operators, where 𝛼 = 𝑖 𝑗, 𝑖 ∈ [1,𝑚], 𝑗 ∈ [1, 𝑛],

𝛼𝑟 =

{𝑖𝑟,where 𝑖 ∈ [1,𝑚], 1 ≤ 𝑟 ≤ 𝑛, if 𝐷 ∈ {𝑆, 𝑁 }𝑟𝑖,where 1 ≤ 𝑟 ≤ 𝑚, 𝑖 ∈ [1, 𝑛], if 𝐷 ∈ {𝐸,𝑊 }.

• 𝑨𝑫𝜶𝒓

: 𝑟𝑡ℎ arterial for traffic in direction 𝐷 (Figure 1).

• 𝑳𝑫∗𝜶 : a link within an arterial such that multiple links connect

consecutive intersections to form an arterial. Here, ∗ denotes oneor more lanes within each link and is dropped when the context

is clear (Figure 1).

• 𝑰𝜶 : an intersection within the𝑚 × 𝑛 network (Figure 1).

• 𝑰𝒓𝒓 ′ : intersection formed by arterials 𝐴𝐷𝛼𝑟

and 𝐴𝐷′𝛼𝑟 ′ (Figure 1).

Traffic lights at each intersection within the network allow only

the non-conflicting flows to enter and access the intersection at

once, as per the phase sequences.Similar to [25, 26], our model considers that the traffic flow

within the𝑚 × 𝑛 network is managed by a traffic manager (TM),

denoted by 𝑇𝑀𝑚,𝑛 , that aggregates real-time traffic information

within the network from traffic sensors, forecast data and/or from

neighboring TMs. The TMs then control the traffic lights as per

some traffic control technique. We assume that the relevant data is

made available to the TM through minimal connectivity between

the intersections. Explicitly defining how such data is acquired

is out of scope of this work. The connected infrastructure is also

2

Timely and Non-Disruptive Response of Emergency Vehicles: A Real-Time Approach RTNS’2021, April 7–9, 2021, NANTES, France

Table 1: Glossary of notationsNotation Description

𝑻𝒄 Traffic cycle length (Sec. 3.2).

𝒂𝑫𝜶 , 𝒒𝑫𝜶 , 𝒛𝑫𝜶 Arrival rate, vehicle queue and the capacity of link 𝐿𝐷𝛼 (Sec. 3.2).

𝒍𝑫𝜶 , 𝒗𝒍 , 𝒅𝒔𝒂𝒇 𝒆Length of the link 𝐿𝐷𝛼 , vehicle length and

safe distance between consecutive vehicles (Sec. 3.2).

𝒉, 𝒕𝒍 Saturation headway and lost time [11].

𝒏𝑫𝜶,𝒌

, 𝑻𝒌Number of vehicles discharged in the 𝑘𝑡ℎ traffic cycle

from the link 𝐿𝐷𝛼 , and the time taken for the same(Equation 1).

𝒗𝒆 , 𝒍𝒆 , 𝒔𝒆 , 𝝅𝒆 , 𝜹Emergency response vehicle (ERV), location coordinates, the desired

speed, the priority level and delay tolerance of the ERV (Sec. 3.3).

𝑺𝑺 , 𝑩𝑺 , 𝑻𝑺 Sporadic server, its assigned budget and its inter-arrival time (Sec. 5.1).

𝑰 𝒆 , 𝑳𝒆The list of coordinates of the intersections and links

along the ERV route (Sec. 5.2).

𝑳𝑫1 , 𝑳𝑫𝝀

The first and the _𝑡ℎ link coordinates on the ERV’s route (Sec. 5.2).

𝝉𝒆 , 𝒂𝒆 , 𝒅𝒆ERV task, the arrival time and the deadline for the ERV task (Sec. 5.2).

𝒋𝒆𝒊 , 𝒂𝒆𝒊 , 𝑪

𝒆𝒊 , 𝒅

𝒆𝒊

𝑖𝑡ℎ sub-job of the ERV task, the arrival time,

the execution time and the deadline of the 𝑖𝑡ℎ sub-job (Sec. 5.2).

𝑼𝑫𝜶 % utilization for the server at link 𝐿𝐷𝛼 .

𝑼𝑫𝒄𝜶

% utilization such that𝑈𝐷𝑐𝛼 = 𝑈𝑆

𝛼 = 𝑈𝑁𝛼 , if 𝐷𝑐 = 𝑆𝑁 ,

and𝑈𝐷𝑐𝛼 = 𝑈𝑆

𝛼 = 𝑈𝑊𝛼 , otherwise (Sec. 5.3).

𝑼𝑫𝒄𝒎𝒊𝒏𝜶

, 𝑼𝑫𝒄𝒎𝒂𝒙𝜶 Minimum and maximum utilization demands (Sec. 5.3).

𝒕𝒔𝒕𝒂𝒓𝒕 , 𝒕𝒏𝒘Time of receiving the ERV arrival information

and duration between 𝑡𝑠𝑡𝑎𝑟𝑡 and 𝑑𝑒 (the ERV deadline) (Algorithm 2).

𝒏𝒏𝒘 , 𝒕𝒄𝒍𝒆𝒂𝒓Total vehicles expected within 𝑡𝑛𝑤and time to clear the vehicles respectively (Algorithm 2).

𝒒𝒆𝒊 Vehicle queue in the links during compensation phase (Algorithm 3).

𝑼𝑫𝒄𝜶𝒆 , 𝑼

𝑫′𝒄

𝜶𝒆% utilization for the complementary server pairs along the ERV route

and the server pairs along the links conflicting the ERV route (Sec. 5.3).

used to acquire ERV information which will be discussed in de-

tail (Section 5.2). Additionally, the size of the 𝑚 × 𝑛 network is

determined as per the feasibility of reliable connectivity among

the traffic infrastructure, communication latency overhead, avail-

able computational resources to perform calculations in real-time

and the traffic signal coordination requirements as per the U.S.

Department of Transportation guidelines [22].

3.2 Non-Emergency Traffic FlowThe traffic lights at each intersection within the network change

between green-yellow-red states as per the assigned timings. Each

traffic light changes its state once in a cyclic pattern based on the

phase sequence and cycle time (𝑇𝑐 ). With some connectivity among

the traffic infrastructure, multiple intersections can be coordinated,

especially in tightly-spaced urban traffic environment, such that all

intersections within the purview of a TM have a fixed𝑇𝑐 value [22].

The phases of the traffic lights at consecutive intersections are then

activated based on the traffic control technique to avoid queue spill-

backs and reduce traffic wait-times [26]. An incoming link 𝐿𝐷𝛼 is

𝑳𝟏𝟏𝑬 𝑳𝟏𝟐

𝑬 𝑳𝟏𝟑𝑬

𝑳𝟐𝟏𝑬 𝑳𝟐𝟐

𝑬 𝑳𝟐𝟑𝑬

𝑳𝟑𝟏𝑬 𝑳𝟑𝟐

𝑬 𝑳𝟑𝟑𝑬

𝑳𝟏𝟏𝑾 𝑳𝟏𝟐

𝑾 𝑳𝟏𝟑𝑾

𝑳𝟐𝟏𝑾 𝑳𝟐𝟐

𝑾 𝑳𝟐𝟑𝑾

𝑳𝟑𝟏𝑾 𝑳𝟑𝟐

𝑾 𝑳𝟑𝟑𝑾

𝑳𝟑𝟏

𝑺𝑳𝟐𝟏

𝑺𝑳𝟏𝟏

𝑺

𝑳𝟑𝟐

𝑺𝑳𝟐𝟐

𝑺𝑳𝟏𝟐

𝑺

𝑳𝟑𝟑

𝑺𝑳𝟐𝟑

𝑺𝑳𝟏𝟑

𝑺

𝑳𝟏𝟑

𝑵𝑳𝟐𝟑

𝑵𝑳𝟑𝟑

𝑵

𝑳𝟏𝟐

𝑵𝑳𝟐𝟐

𝑵𝑳𝟑𝟐

𝑵

𝑳𝟏𝟏

𝑵𝑳𝟐𝟏

𝑵𝑳𝟑𝟏

𝑵

𝑰𝟏𝟏 𝑰𝟏𝟐 𝑰𝟏𝟑

𝑰𝟐𝟏 𝑰𝟐𝟐 𝑰𝟐𝟑

𝑰𝟑𝟏 𝑰𝟑𝟐 𝑰𝟑𝟑

𝑨𝜶𝟏𝑬

𝑨𝜶𝟐𝑬

𝑨𝜶𝟑𝑬

𝑨𝜶𝟏𝑾

𝑨𝜶𝟐𝑾

𝑨𝜶𝟑𝑾

𝑨𝜶𝟏

𝑺

𝑨𝜶𝟐

𝑺

𝑨𝜶𝟑

𝑺

𝑨𝜶𝟏

𝑵

𝑨𝜶𝟐

𝑵

𝑨𝜶𝟑

𝑵

Figure 1: A typical 3 × 3 road network [26]

ERV dispatch

Calculate ERV arrival time

and deadlines (Alg. 1)

TM activates

Optimize network-wide traffic lights as

per mechanism (Sec. 5.4)

Select ERV preemption mechanism

(Alg. 2)

Find additional delay tolerance

using triage scale (Tab.1)

ERV passed?Trigger recovery

phase (Sec. 5.4.3)Proactive Preemption Critical Preemption

•100% budget for servers with ERV task•0% budget for conflicting servers

Mechanism as per Algorithm 2

•Reserved budget for servers with ERV task as per priority•Allow conflicting flows to avoid long queues during ERV traversal

Figure 2: TM task flow and preemption mechanisms

characterized by the tuple {𝑎𝐷𝛼,𝑘

, 𝑞𝐷𝛼,𝑘

, 𝑧𝐷𝛼 }, where 𝑎𝐷𝛼,𝑘 is the incom-

ing non-emergency vehicle flow rate, 𝑞𝐷𝛼,𝑘

is the number of vehicles

queued in the link during the 𝑘𝑡ℎ traffic cycle, and 𝑧𝐷𝛼 is the linkcapacity, i.e., the maximum number of vehicles that can enter a

link before spillback occurs, and the remaining notations are as

explained earlier. As per [25], the link capacity can be estimated

as 𝑧𝐷𝛼 =𝑙𝐷𝛼

𝑣𝑙+𝑑𝑠𝑎𝑓 𝑒 , where 𝑙𝐷𝛼 is the length of the link 𝐿𝐷𝛼 and 𝑣𝑙 and

𝑑𝑠𝑎𝑓 𝑒 denote the average vehicle length and safe distance required

between any two consecutive vehicles, respectively. The incoming

non-emergency vehicle flow rate, 𝑎𝐷𝛼,𝑘(𝑡) is a time-varying quantity,

however, in a given traffic cycle, under dynamic traffic conditions,

the worst-case traffic flow can be bounded based on traffic infor-

mation from the intersections. We thus refer to 𝑎𝐷𝛼,𝑘(𝑡) as 𝑎𝐷

𝛼,𝑘for

the rest of the paper to determine non-ERV flow rates. When the

traffic lights change and vehicles are allowed to cross the intersec-

tion, the discharge pattern is represented by the saturation headwaymodel [31] and is given by,

𝑇𝑘 = ℎ · 𝑛𝐷𝛼,𝑘+ 𝑡𝑙 . (1)

Here, 𝑇𝑘 denotes the time required to discharge 𝑛𝐷𝛼,𝑘

vehicles from

link 𝐿𝐷𝛼 during the 𝑘𝑡ℎ traffic cycle when the saturation headway

ℎ = 2 s and the lost time 𝑡𝑙 = 4 s are considered, respectively [11].

3.3 Emergency Response VehiclesThe emergency vehicles are often guided by a back-end dispatch

system with various routing mechanisms to calculate the optimum

path from its origin to the emergency location [29]. By leveraging

V2X connectivity between the ERV (or the back-end system) and

the connected infrastructure, the intersections within our𝑚 × 𝑛road network that will be affected by the ERV traversal can be

identified in advance. The ERVs’ arrival information can then be

disseminated to the TM to allow safe and timely traversal of the ERV.

In our model, an incoming ERV is denoted by 𝑣𝑒 and is represented

by the tuple, {𝑙𝑒 , 𝑠𝑒 , 𝜋𝑒 }. Here, 𝑙𝑒 , 𝑠𝑒 , and 𝜋𝑒 denote the current lo-cation coordinates, the desired speed and the priority level of an

ERV. We schedule the traffic such that the ERV maintains its fixed

desired speed. The arrival times and the deadlines are assigned to

the ERV based on the priority level defined by the triage scale [9].

Preempting multiple ERVs at once is left for future work.

Setting priorities as per the triage levels. Triage scale [9] providescritical ERV information that is already being utilized in emergency

and disaster management to establish prioritized time frames for

3

RTNS’2021, April 7–9, 2021, NANTES, France Oza et al.

𝝉𝟏(2,4)

𝝉𝟐(4,7)𝝉𝟑(5,8)

Aperiodic Tasks 𝝉𝒊(𝒓𝒊, 𝒄𝒊)

Sporadic Server

𝑺𝑺(𝑩𝑺, 𝑻𝑺)

Aperiodic Task Queue

Traffic Manager Task 𝑻𝑴𝒎,𝒏(𝑪𝑻𝑴, 𝒂𝑻𝑴)

Intersection(Shared Resource)

Figure 3: Real-time task model for an intersection in a roadnetwork [26]

emergencies. Since the ERV response time is directly influenced

by the traffic conditions, it is crucial to utilize this data in traffic

planning as well [7]. In our approach, we relate each urgency level

to a priority value and a delay tolerance (Table 2). The lower the

priority value, the smaller the delay tolerance for the ERV to cross

our𝑚 × 𝑛 network. When 𝜋𝑒 = 1, the ERV must travel as quickly

as possible (zero delay tolerance) and any additional delay may

lead to missed target response time. However, for lower priorities

(larger 𝜋𝑒 value), we can slightly delay the ERV travel through our

network (corresponding 𝛿 value) and still meet the ERV deadlines

while allowing the conflicting flows to cross the intersections.

4 SYSTEM OVERVIEWAs discussed in Section 2, the existing preemption strategies deploy

a green wave to facilitate ERV traversal. However, its greedy mech-

anism leads to spillbacks in the road network. With the real-time

task scheduling approach presented in this paper, by providing

the timeliness guarantees of a real-time approach, we need not

necessarily enable the green wave as soon as an ERV is detected to

facilitate its traversal. By leveraging connectivity among the traffic

infrastructure and real-time traffic information, we can proactivelypreempt the ERV traversal such that the ERV deadlines are met.

Further, some additional green time can also be provided to the

conflicting flows using an optimal strategy to minimize the queues

caused by ERV preemption.

As mentioned in Section 3, the traffic manager (TM) is responsi-

ble to acquire real-time traffic and ERV information to control the

traffic lights within the entire network. When an ERV dispatch in-

formation arrives, the traffic manager (TM) obtains the priority and

the delay tolerance for the ERV as per the triage scale (Table 2). The

TM then calculates the arrival time and the deadline for the ERV

task (Algorithm 1). Depending on the arrival time of the ERV and

the traffic conditions within the network, our proposed approach

selects a suitable preemption mechanism (Figure 2).

Proactive preemption provides timeliness guarantees for the ERV

preemption while also optimally managing the traffic through the

network before and during the ERV traversal. By providing addi-

tional green times to the conflicting traffic flows, this approach not

only guarantees ERVs response times as per their priority, but also

reduces traffic delays across the network.

Critical preemption is triggered when the traffic flow in the net-

work is heavy and the ERV deadline does not allow for a proactivepreemption. Our critical preemption approach enables green wave

Table 2: Relating triage scale with traffic delay tolerance

Urgency Status

Assessment

TimePriority (𝜋𝑒 )

Traffic Delay

Tolerance (s)Example (s)

Resuscitation 0 minutes 1 𝛿1 0

Emergent 15 minutes 2 𝛿2 45

Urgent 30 minutes 3 𝛿3 90

Less Urgent 60 minutes 4 𝛿4 135

Nonurgent 120 minutes 5 𝛿5 180

through the arterial that the ERV traverses, while optimally adjust-

ing the traffic flow for the rest of the network to accommodate for

the green wave to alleviate its impacts on traffic delays.

Depending on the chosen preemption mechanism for the inter-

sections impacted by the ERV traversal (Algorithm 2), an optimalnetwork-wide strategy is formulated to avoid spillbacks and maxi-

mize traffic flow (Section 5). The preemption is active until the ERV

safely passes through the road network and its deadlines are met.

We then activate our recovery phase (Section 5.4), where we modify

the per-arterial recovery approach presented in [26] to stabilize

traffic across the network where we provide additional green times

to the links prone to spillbacks. Once the traffic operations are back

to normal and there are no ERV traversal requests, the TM enables

a default traffic strategy, such as [26]. As per results (Section 6), our

approach ensures that the ERV travel time is not hampered while

reducing the traffic delays in the network.

5 REAL-TIME SCHEDULING OF EMERGENCYVEHICLES THROUGH A ROAD NETWORK

We model an𝑚 × 𝑛 road network (Figure 1) controlled by a traffic

manager, 𝑇𝑀𝑚,𝑛 , that schedules non-emergency traffic and emer-

gency vehicles through this network, as a set of real-time tasks. We

first describe the real-time task model in [26] for traffic flow control

through an𝑚 × 𝑛 network, but lacks the preemption mechanisms

and modelling of emergency vehicles.

5.1 Review of Real-Time Task Model for aNetwork of Intersections

As shown in Figure 3, the non-emergency vehicles are represented

as aperiodic tasks (𝜏𝑖 ) that have unknown arrival times (𝑟𝑖 ) andknown execution times (𝑐𝑖 ) as per the traffic flow rates and the

saturation headway model to travel though the intersections, re-

spectively. If the traffic lights are red, the vehicles form a queue

until the lights turn green. This resembles aperiodic tasks (vehi-

cles) joining an aperiodic task queue (links) waiting to be executed

on the shared resource (intersections). Since the traffic lights at

each intersection modulate the vehicle flow, they are equivalent to

sporadic servers (𝑆𝑆 ) serving each task queue as per the assigned

budget (𝐵𝑆 ) and its inter-arrival time (𝑇𝑆 ) [8]. The budget and the

arrival time for each sporadic server is decided by the traffic man-

ager task (𝑇𝑀) at the start of each traffic cycle. For example, in an

𝑚 × 𝑛 traffic network, with each intersection having four incoming

flows from each direction 𝐷 ∈ {𝑁, 𝐸,𝑊 , 𝑆}, there are𝑚𝑛 shared re-

sources, 4𝑚𝑛 aperiodic task queues and therefore, sporadic servers

managed by the 𝑇𝑀𝑚,𝑛 task. The budgets at each intersection are

assigned by the 𝑇𝑀𝑚,𝑛 task such that no two conflicting flows get

to enter into the intersections at once and thereby ensuring safety.

4

Timely and Non-Disruptive Response of Emergency Vehicles: A Real-Time Approach RTNS’2021, April 7–9, 2021, NANTES, France

Algorithm 1: Calculating the ERV task parameters: arrival

time and deadline using Manhattan distance [33]

Input :𝐿𝐷1, 𝐿𝐷

_⊲ coordinates to the entry and exit points of the preemption

arterial

𝑙𝑒 , 𝑠𝑒 , 𝜋𝑒 ⊲ ERV parameters

Output :𝑎𝑒 , 𝑑𝑒 ⊲ arrival time and deadline for 𝜏𝑒

1 Function GetERVTaskParams(𝐿𝐷1, 𝐿𝐷

_, 𝑙𝑒 , 𝑠𝑒):

2 𝑑𝑖𝑠𝑡1 = ManhattanDistance(𝐿𝐷1, 𝑙𝑒 ) ⊲ distance to 𝐿𝐷

1

3 𝑑𝑖𝑠𝑡_ = ManhattanDistance(𝐿𝐷_, 𝑙𝑒 ) ⊲ distance to 𝐿𝐷

_

4 𝛿 = GetDelay(𝜋𝑒) ⊲ From Table 2

5 𝑎𝑒 =𝑑𝑖𝑠𝑡

1

𝑠𝑒⊲ arrival time as per desired speed

6 𝑑𝑒 =𝑑𝑖𝑠𝑡_𝑠𝑒+ 𝛿 ⊲ deadline as per triage scale

7 return 𝑎𝑒 , 𝑑𝑒

8 End Function

The servers arrive as per their arrival times are executed on the

shared resource until the assigned budget is exhausted.

5.2 Emergency Vehicles as Real-Time TasksThe following information is required by the TM in our approach. (i)

The route that the ERVwill access within our𝑚×𝑛 network, and (ii)

the information represented by the tuple {𝑙𝑒 , 𝑠𝑒 , 𝜋𝑒 } that containsthe location coordinates, the desired speed, and the priority level of

the ERV, respectively. Explicitly defining how such information is

made available to the TM is out of scope of this work, however, we

rely on existing communication between connected infrastructure,

connected ERVs and/or the back-end dispatch systems that plan for

the ERV’s route and response times. Since the arrival of the ERV is

at random, it resembles an aperiodic task.From the route information, the TM determines the location

coordinates of the intersections (𝐼𝑒 ) and links (𝐿𝑒 ) that the ERV will

traverse. For simplicity of representation, we assume that the ERV

traverses only in the east-west or the north-south direction through

our road network, similar to the non-emergency traffic. However,

our approach is applicable to the general case. For example, consider

an ERV 𝑣𝑒 , entering a 3×3 network (Figure 1) and traveling throughthe arterial 𝐴𝐷

𝛼2

. The intersections and links accessed by the ERV

are 𝐼𝑒 = {𝐼21, 𝐼22, 𝐼33} and 𝐿𝑒 = {𝐿𝐷1, 𝐿𝐷

2, 𝐿𝐷

3}, respectively. Thus

the TM task must assign the budget to the servers that serve the

links 𝐿𝐷1, 𝐿𝐷

2, and 𝐿𝐷

3to facilitate preemption.

The ERV task 𝜏𝑒 is represented by the tuple {𝑎𝑒 , 𝑑𝑒 } where 𝑎𝑒and 𝑑𝑒 denote the arrival time and the deadline of ERV task. The

arrival time indicates the time at which the ERV is expected to enter

our road network, and the deadline indicates the time before which

the ERV must exit our network to meet its priority-based response

time. The values of 𝑎𝑒 and 𝑑𝑒 are calculated by the TM task using

Algorithm 1. Since the𝑇𝑀 task is responsible to schedule non-ERV

traffic while also facilitate ERV traversals arriving at random, it

resembles an aperiodic task with unknown arrival time and fixed

execution times that assigns the server budgets (Figure 3).

The ERV task’s deadline is calculated as per the delay tolerance

for each urgency level (Algorithm 1). If the ERV has the highest

priority, it has no delay tolerance (𝛿1 = 0, as per Table 2). Therefore,

the deadline for a highest priority ERV task is equal to the travel

time of the ERV from its current location to the end of the network

at its desired speed (Line 6). The TM task schedules the non-ERV

Aperiodic Task𝝉𝒆(𝒂𝒆, 𝒅𝒆)

Sub-Job 𝒋𝟏𝒆(𝒂𝟏

𝒆 , 𝑪𝟏𝒆 , 𝒅𝟏

𝒆)Sub-Job

𝒋𝟐𝒆(𝒂𝟐

𝒆 , 𝑪𝟐𝒆 , 𝒅𝟐

𝒆)Sub-Job

𝒋𝟑𝒆(𝒂𝟑

𝒆 , 𝑪𝟑𝒆 , 𝒅𝟑

𝒆)

𝒂𝒆 = 𝒂𝟏𝒆

𝑪𝟏𝒆 𝑪𝟐

𝒆 𝑪𝟑𝒆

Time in 𝑳𝟐𝟏𝑬 + 𝑰𝟐𝟏 Time in 𝑳𝟐𝟐

𝑬 + 𝑰𝟐𝟐 Time in 𝑳𝟐𝟑𝑬 + 𝑰𝟐𝟑

𝒂𝟐𝒆 𝒂𝟑

𝒆 𝒅𝟑𝒆 = 𝒅𝒆

Time (s)

𝒂𝒆, 𝒅𝒆: arrival time and deadline of ERV task 𝝉𝒆

𝒂𝒊𝒆, 𝑪𝒊

𝒆, 𝒅𝒊𝒆 :

arrival time, execution time and deadline of sub-job 𝒋𝒊

𝒆

Figure 4: Modelling an ERV as an aperiodic real-time taskand its sub-jobs

traffic and the ERV through the network such that the ERV meets

the deadline since its failure leads to increased response times to

attend life-threatening emergencies.

To capture an ERV traversing through the arterial 𝐴𝐷𝛼𝑟

in a real-

time model, each ERV task 𝜏𝑒 consists of _ sub-jobs 𝑗𝑒𝑖,∀𝑖 ∈ [1, _]

where _ = 𝑛 if𝐷 ∈ {𝐸,𝑊 } and _ =𝑚 otherwise. Here, the execution

of the 𝑖𝑡ℎ sub-job 𝑗𝑒𝑖represents traversal of ERV in the link 𝐿𝐷

𝑖𝑟until it crosses the intersection 𝐼𝑖𝑟 . Each sub-job 𝑗𝑒

𝑖is represented

by the tuple, {𝑎𝑒𝑖,𝐶𝑒

𝑖, 𝑑𝑒

𝑖} denoting the arrival time, the execution

time and the deadline of the 𝑖𝑡ℎ sub-job, respectively. As shown in

Figure 4, the arrival time of the sub-job indicates approaching ERV,

the execution time indicates the time the ERV takes to traverse the

corresponding section of the route, and the deadline indicates the

time before which the sub-job must complete execution to avoid

missed ERV response times.

Property 1. An ERV task 𝜏𝑒 consisting of _ sub-jobs 𝑗𝑒1, 𝑗𝑒2, . . . , 𝑗𝑒

_,

has the following properties: (i) The arrival time 𝑎𝑒1of the sub-job 𝑗𝑒

1

is equal to the arrival time 𝑎𝑒 of the task 𝜏𝑒 . (ii) The deadline 𝑑𝑒_of

the sub-job 𝑗𝑒_is equal to the deadline 𝑑𝑒 of the task 𝜏𝑒 . And finally,

(iii) the arrival time 𝑎𝑒𝑖of the sub-job 𝑗𝑒

𝑖is equal to the completion

time of the previous sub-job 𝑗𝑒𝑖−1, 𝑖 = 2, . . . , _.

Property 1 ensures that the entire trajectory of the ERV is ac-

counted for by our real-time model. (i) and (ii) ensure that the

network-level arrival times and the deadlines of the ERV are trans-

lated to is sub-jobs. If the first sub-job 𝑗𝑒1arrives at any time after

the actual ERV arrival time, this means that the ERV is not being

promptly serviced, which could lead to delay, abrupt stop and go

movements, and unsafe driving conditions for the ERV. Alternately,

if the last sub-job 𝑗𝑒_has a deadline earlier than the task itself, the

ERV will have to travel faster than its desired speed to meet its

deadline leading to safety violations. Similarly, (iii) ensures the

continuity of the ERV’s trajectory. The 𝑖𝑡ℎ sub-job must arrive as

soon as the 𝑖-1𝑡ℎ (previous) sub-job completes execution (Figure 4)

to maintain the continuity of the ERV traversal without abruptly

stopping inside the intersection box.

Assigning local deadlines to the sub-jobs: From Figure 4, the

ERV task 𝜏𝑒 will meet its deadline only if each of its sub-job meet

their respective deadlines. Once the TM receives the ERV informa-

tion, we assign the deadlines to each sub-job to maintain the overall

deadline for the ERV task as per Lemma 1.

Lemma 1. Consider an ERV task 𝜏𝑒 with the arrival time anddeadline of 𝑎𝑒 and 𝑑𝑒 respectively, representing ERV traversal throughan 𝑚 × 𝑛 road network across the arterial 𝐴𝐷

𝛼𝑟, with _ sub-jobs 𝑗𝑒

𝑖

𝑖 = 1, . . . , _ corresponding to each segment consisting of the link 𝐿𝐷𝑖

5

RTNS’2021, April 7–9, 2021, NANTES, France Oza et al.

Servers for ERV

Servers for conflicting flow

𝒅𝒆𝒂𝟑𝒆𝒂𝟐

𝒆𝒂𝟏𝒆

𝒂𝟑𝒆𝒂𝟐

𝒆𝒂𝟏𝒆 𝒅𝒆

𝝅𝒆 = 𝟓

𝝅𝒆 = 𝟏

No conflicting server execution due to highest priority

Delayed deadline for lower priority with conflicting server execution

Delayed deadline due to lower priorityavoiding possible

spillbacks and congestion in

conflicting flows

Time (s)

Time (s)

Figure 5: An example server execution for ERV preemptionwith varying priorities

and intersection 𝐼𝑖𝑟 . If the traffic flow rate from each direction 𝐷 atthe intersection 𝐼𝑖𝑟 is given by 𝑎𝐷

𝑖𝑟, then the local deadline 𝑑𝑒

𝑖for the

𝑖𝑡ℎ sub-job is given by,

𝑑𝑒𝑖 ∝∑

𝐷∈{𝑁,𝐸,𝑊 ,𝑆 }𝑎𝐷𝑖 , (2)

such that,_∑𝑖=1

𝑑𝑒𝑖 = 𝑑𝑒 , (3)

where, _ =𝑚 if 𝐷 ∈ {𝑆, 𝑁 } and 𝑛 otherwise.

Proof: The higher the traffic flow in a link, the longer will be

the execution time of the corresponding sub-job (Figure 4). To

ensure that there is fair distribution of time to execute the sub-

jobs, the local deadlines must be proportional to the traffic flows

within the intersection (and hence the link). As per Equation 2,

a later deadline will be assigned to the sub-job if the net traffic

flow rate through an intersection is higher. Similarly, since the

arrival times of the sub-jobs are co-dependent as shown in the

Property 1, missing the deadline for one sub-job causes a cascading

effect and end-to-end deadline misses. If the summation of all the

local deadlines is less than the total end-to-end deadline, the ERV

may traverse quickly through the road network, but the conflicting

flows suffer from resource starvation. Alternately, if the summation

of the local deadlines is greater than the total end-to-end deadline

it would clearly lead to missed end-to-end deadlines due to the sub-

job precedence established in Property 1. Therefore, the deadline

distribution in Equation 2 must be constrained by Equation 3.

As shown in Figure 5, an ERV with a lower priority has a higher

delay tolerance, hence its deadline is later than that of the ERV

with the highest priority. Upon scheduling, while the ERV with the

highest priority must be executed as soon as it arrives, a lower pri-

ority ERV task execution can be delayed to schedule the conflicting

flows and still meet the deadline. With this task model for the ERV

and the non-ERV traffic, we now discuss the scheduling strategy to

provide timely traversal of the ERV through the road network.

5.3 Non-emergency Traffic Flow SchedulingWhen there is no ERV dispatched, the TM deploys a default traffic

control scheme. For our work, we use the network-wide traffic

control strategy provided in [26] as a default scheme. However, any

schedule-based traffic strategy maybe deployed at the TM. We now

briefly summarize the budget allocation strategy provided in [26]

and then provide the requirements to accommodate the ERVs.

Algorithm 2: Preemption mechanism based on ERV dead-

line and traffic flow

Input :𝑡𝑠𝑡𝑎𝑟𝑡 ⊲ ERV dispatch notification received

𝑎𝑒 , 𝑑𝑒 , 𝜋𝑒 ⊲ ERV arrival time, deadline and priority

{𝑎𝐷𝑖, 𝑞𝐷

𝑖, 𝑧𝐷

𝑖} ⊲ traffic of links in preemption arterial

Output :preemption ⊲ selected mechanism

1 Function SelectPreemption(𝑡𝑠𝑡𝑎𝑟𝑡 , 𝑎𝑒 , 𝑑𝑒 , 𝑎𝐷

𝑖, 𝑞𝐷

𝑖):

2 𝑡𝑛𝑤 = 𝑑𝑒 − 𝑡𝑠𝑡𝑎𝑟𝑡3 𝑛𝑎𝑟𝑟 = 𝑎𝐷

1𝑡𝑛𝑤 ⊲ vehicles expected to arrive within 𝑡𝑛𝑤

4 𝑞𝑠𝑢𝑚 =∑_

𝑖=1 𝑞𝐷𝑖

⊲ total vehicles in queue at 𝑡𝑠𝑡𝑎𝑟𝑡5 𝑛𝑛𝑤 = 𝑛𝑎𝑟𝑟 + 𝑞𝑠𝑢𝑚 ⊲ total vehicles expected within 𝑡𝑛𝑤6 𝑡𝑐𝑙𝑒𝑎𝑟 = 𝑛𝑛𝑤ℎ + 𝑡𝑙 ⊲ time to clear 𝑛𝑛𝑤 vehicles (Eq. 1)

7 if 𝑎𝑒 − 𝑡𝑠𝑡𝑎𝑟𝑡 > 𝑡𝑐𝑙𝑒𝑎𝑟 then8 return proactive preemption

9 else10 return critical preemption

11 End Function

In [26], the TM gathers the real-time traffic information from

each intersection within the 𝑚 × 𝑛 network and allocates some

budget and the arrival times for the sporadic servers in the network

such that no two conflicting flows enter the intersections at the

same time. For a non-emergency traffic flow only, there is no priority

involved and therefore all sporadic servers arrive at the same time,

at the start of each traffic cycle and are executed on the shared

resource in a round-robin fashion. As mentioned, when there is no

ERV arrival, for our approach, the TM controls the non-emergency

traffic using the strategy defined in [26] which ensures that all

traffic lights within the𝑚 ×𝑛 network are optimally managed such

that spillbacks do not occur at any place within the network, when

possible. To do so, the budget allocation across all the servers in

the network for each traffic cycle is formulated as an optimization

problem with the following objective and constraints:

maximize

∑𝑖=1...𝑚,𝑗=1...𝑛,

𝐷𝑐 ∈{𝑆𝑁,𝐸𝑊 }

𝑈𝐷𝑐𝛼 (4)

subject to𝑈𝐷𝑐

𝑚𝑖𝑛𝛼≤ 𝑈

𝐷𝑐𝛼 ≤ 𝑈

𝐷𝑐𝑚𝑎𝑥𝛼 , (5)

𝑈𝐷𝑐

𝛼−1 −𝑈𝐷𝑐𝛼 ≤ 𝑧

𝐷𝑐𝛼 ℎ

𝑇𝑐, (6)∑

𝐷𝑐 ∈{𝑆𝑁,𝐸𝑊 }𝑈𝐷𝑐𝛼 ≤ 1, (7)

where,𝑈𝐷𝑐

𝑚𝑖𝑛𝛼=ℎ · (𝑎𝑘 ·𝑇𝑐 + 𝑞𝑘 − 𝑧) + 𝑡𝑙

𝑇𝑐, (8)

𝑈𝐷𝑐𝑚𝑎𝑥𝛼 =

ℎ · (𝑎𝑘 ·𝑇𝑐 + 𝑞𝑘 ) + 𝑡𝑙𝑇𝑐

. (9)

Here, 𝑈𝐷𝑐

𝑚𝑖𝑛𝛼and 𝑈

𝐷𝑐𝑚𝑎𝑥𝛼 correspond to the minimum and the

maximum utilization demands for the server pairs at the inter-

sections 𝐼𝛼 , respectively. The minimum utilization demand is the

budget required to avoid spillbacks within any given link, while the

maximum demand represents the budget to dispatch all vehicles

and clear a link. Similarly,𝑈𝐷𝑐𝛼 corresponds to the assigned budget

for the server pairs at intersection 𝐼𝛼 . Since two non-conflicting

flows can access the intersection at once, 𝑈 𝑆𝑁𝛼 = 𝑈 𝑆

𝛼 = 𝑈𝑁𝛼 and

𝑈 𝐸𝑊𝛼 = 𝑈 𝐸

𝛼 = 𝑈𝑊𝛼 . Since the budget allocation translates to the

6

Timely and Non-Disruptive Response of Emergency Vehicles: A Real-Time Approach RTNS’2021, April 7–9, 2021, NANTES, France

Algorithm 3: Queues for ERV compensation phase

Input :𝑡𝑠𝑡𝑎𝑟𝑡 ⊲ ERV dispatch notification received

{𝑎𝑒𝑖}, {𝑑𝑒

𝑖} ⊲ arrival time and deadline of all sub-jobs

{𝑎𝐷𝑖, 𝑞𝐷

𝑖, 𝑧𝐷

𝑖} ⊲ traffic of links in preemption arterial

𝑇𝑐 ⊲ traffic cycle time

Output : {𝑞𝑒𝑖} ⊲ set of queues for each link

1 Function GetQueues(𝑡𝑠𝑡𝑎𝑟𝑡 , {𝑎𝑒𝑖 }, {𝑑𝑒𝑖 }, 𝑎𝐷𝑖 , 𝑞𝐷𝑖, 𝑧𝐷

𝑖,𝑇𝑐):

2 𝑡𝑟 = (𝑑𝑒1− 𝑡𝑠𝑡𝑎𝑟𝑡 )%𝑇𝑐

3 𝑛𝑒𝑐 =

⌊𝑑𝑒1−𝑡𝑠𝑡𝑎𝑟𝑡𝑇𝑐

⌋4 if 𝑡𝑟 < 𝑡𝑙 then5 𝑡𝑟+ = 𝑇𝑐 , 𝑛

𝑒𝑐− = 1

6 ⊲ 𝑡𝑙 : human reaction lost time

7 𝑛𝑟 =𝑡𝑟 −𝑡𝑙ℎ

8 𝑛𝑟𝑖𝑛 = 𝑎𝐷1𝑡𝑟

9 𝑞𝑒1← min(𝑛𝑟 − 𝑛𝑟𝑖𝑛 , 𝑧

𝐷1)

10 for 𝑖 = 2 . . . _ do11 𝑐𝑒

𝑖−1 = 𝑑𝑒𝑖−1 − 𝑎𝑒𝑖−1

12 𝑞𝑒𝑖← min(

𝑐𝑒𝑖−1−𝑡𝑙ℎ

, 𝑧𝐷𝑖)

13 return {𝑞𝑒𝑖}

14 End Function

green time for the traffic lights, maximizing the total budget al-

location across the network using Equation 4 implies increased

traffic flow and thereby reduce wait times. Similarly, the constraint

in Equation 5 enforces that resource starvation does not occur by

assigning at least the minimum utilization requirement (𝑈𝐷𝑐

𝑚𝑖𝑛𝛼) for

each server, while avoiding over-utilization by keeping the assign-

ment up to the maximum requirement (𝑈𝐷𝑐𝑚𝑎𝑥𝛼 ). The constraint in

Equation 6 ensures that the budget allocation between consecutive

intersections is such that no spillbacks occur in the system, when

possible, thereby avoiding any additional delays and network-wide

gridlocks. Finally, the constraint in Equation 7 ensures that the

assigned budgets at any given intersection do not exceed 100%.

5.4 Enabling ERV Preemption: Scheduling theERV tasks and its Sub-Jobs

As mentioned in Section 4, our goal is to ensure that the ERV meets

its required response time as per the urgency level of the situa-

tion while leveraging the possible delay tolerance of the ERVs to

schedule non-emergency conflicting traffic flows as well (Figure 5).

This avoids spillbacks due to the prolonged red lights for the con-

flicting traffic flows, while adhering to the ERV’s timeliness. To

facilitate ERV preemption through the traffic network, we propose

an ERV-aware traffic control strategy where, when there is no ERV

expected to enter in the network, the default optimal traffic control

strategy as in [26] is implemented. However, an ERV preemption

request may arrive at any time and hence, we deploy a polling

mechanism that constantly checks for ERV dispatch notifications

via the connected infrastructure such as the back-end dispatch sys-

tem, RSUs or an equipped ERV itself. Once a preemption request is

received, as shown in Figure 2, the TM task is activated to enable

an ERV-aware traffic optimization approach which makes budget

allocation and scheduling decisions by selecting one of the two

preemption mechanisms (Algorithm 2), i.e., proactive preemption

or critical preemption. As discussed, selection of the preemption

mechanism depends on the traffic flow as well as the ERV deadlines.

Upon activation, at time 𝑡𝑠𝑡𝑎𝑟𝑡 , the TM calculates the ERV task’s

arrival time (𝑎𝑒 ) and the deadline (𝑑𝑒 ) using Algorithm 1. Let us

consider, that the ERV requests preemption through the arterial

𝐴𝐷𝛼𝑟

to access our network, which comprises of links 𝐿𝐷𝑖with the

parameters {𝑎𝐷𝑖, 𝑞𝐷

𝑖, 𝑧𝐷𝑖} and intersections 𝐼𝑖𝑟 , 𝑖 = 1, . . . , _. Based

on the traffic flow rate (𝑎𝐷𝑖) and existing queues (𝑞𝐷

𝑖) within each

link of the arterial 𝐴𝐷𝛼𝑟, at the time of receiving the ERV informa-

tion (𝑡𝑠𝑡𝑎𝑟𝑡 ), the TM decides which mechanism, i.e., proactive or

critical preemption to trigger. As shown in Algorithm 2, the TM

calculates the duration (𝑡𝑛𝑤 ) between 𝑡𝑠𝑡𝑎𝑟𝑡 and the ERV deadline,

𝑑𝑒 (Line 2). It then estimates the total number of vehicles, 𝑛𝑛𝑤 , and

the corresponding time, 𝑡𝑐𝑙𝑒𝑎𝑟 (as per Equation 1) to dispatch 𝑛𝑛𝑤vehicles and clear the arterial for the ERV traversal (Line 5 and 6).

Finally, if the time taken to clear the network is not less than the

arrival time of the ERV task, we do not have any additional budget

to proactively control the conflicting flows, and critical preemption

must be triggered immediately (Line 7) to meet the deadlines. Else,

the proactive preemption can be safely triggered (Line 9) to alleviate

resource starvation for the conflicting links, while ensuring that

the ERV deadlines are met. As per the selected mechanism, the TM

task now allocates the budget as well as the arrival times for the

corresponding servers that serve the links through which the ERV

passes while optimizing the traffic through the entire network.

By leveraging the connected infrastructure, the TM will be noti-

fied about an incoming ERV, multiple traffic cycles before it enters

the traffic network, i.e, 𝑎𝑒 − 𝑡𝑠𝑡𝑎𝑟𝑡 > 𝑡𝑐𝑙𝑒𝑎𝑟 to maximize the ben-

efits of the proposed proactive compensation. However, in case

𝑎𝑒 − 𝑡𝑠𝑡𝑎𝑟𝑡 ≤ 𝑡𝑐𝑙𝑒𝑎𝑟 , there is not enough bandwidth to proactively

distribute budget for the conflicting flows and critical preemption is

activated. But, by controlling the traffic as per the arrival time and

the deadline of the ERV task and its sub-jobs, and optimizing traffic

for the network instead of a greedy green wave, we ensure that the

ERV traversal is not hampered while reducing overall traffic delays.

5.4.1 Scheduling with critical preemption. Critical preemption indi-

cates that the servers must dedicate their entire resources towards

facilitating the ERV traversal through the network (Figure 2). Let

the arterial throughwhich the ERV requests for traversal be denoted

by 𝐴𝐷𝛼𝑒

with the corresponding servers along the arterial and their

budgets be denoted by 𝑆𝐷𝑐𝛼𝑒 and 𝑈

𝐷𝑐𝛼𝑒 , respectively. The servers that

are serving the conflicting flows to this arterial and the correspond-

ing budgets are hence denoted by 𝑆𝐷′𝑐𝛼𝑒 and 𝑈

𝐷′𝑐𝛼𝑒 , respectively. Once

critical preemption is triggered, the TM employs an ERV-aware

optimization approach to calculate the budget allocation for the

servers within the𝑚 × 𝑛 network, formulated as follows:

maximize

∑𝑖=1...𝑚,𝑗=1...𝑛,𝑖 𝑗∉𝛼𝑒 ,

𝐷𝑐 ∈{𝑆𝑁 ,𝐸𝑊 }

𝑈𝐷𝑐𝛼 (10)

subject to𝑈𝐷𝑐𝛼𝑒 = 1,𝑈

𝐷′𝑐𝛼𝑒 = 0 (11)

𝑈𝐷𝑐

𝑚𝑖𝑛𝛼≤ 𝑈

𝐷𝑐𝛼 ≤ 𝑈

𝐷𝑐𝑚𝑎𝑥𝛼 , 𝛼 ≠ 𝛼𝑒 (12)

𝑈𝐷𝑐

𝛼−1 −𝑈𝐷𝑐𝛼 ≤ 𝑧

𝐷𝑐𝛼 ℎ

𝑇𝑐, 𝛼 ≠ 𝛼𝑒 (13)

Equation (7) .

7

RTNS’2021, April 7–9, 2021, NANTES, France Oza et al.

Here, 𝐷𝑐 , 𝐷′𝑐 ∈ {𝑆𝑁, 𝐸𝑊 } such that, if 𝐷𝑐 = 𝑆𝑁, 𝐷 ′𝑐 = 𝐸𝑊 , else

𝐷𝑐 = 𝐸𝑊 ,𝐷 ′𝑐 = 𝑆𝑁 . Since the main goal of ERV preemption is not

maximizing traffic flow but to facilitate ERV traversal first, through

the intersections the ERV passes through, the objective function

(Equation 10) only maximizes the traffic flow through the network

for the servers that are not serving the ERV task (𝑖 𝑗 ∉ 𝛼𝑒 ). Since the

arterial 𝐴𝐷𝛼𝑒

is impacted by ERV preemption, all servers along this

arterial are directly assigned 100% of the budget to facilitate rapid

traversal of the ERV (Equation 11). Further, the TM does not assign

any budget to the servers for the conflicting traffic flows to ensure

the safety of the ERV. Constraints given by the Equations 12 and 13

ensure that the rest of the network stays live and the flow is still

maximized while avoiding under-/over-utilization of the resources

and spillbacks. This ensures that the effect of the ERV preemption

remains localized and does not spread through the network as much

as possible. Finally, the schedulability constraint (Equation 7) that

ensures traffic safety is enforced for all servers within the network.

5.4.2 Scheduling in proactive preemption. Proactive preemption is

activated, as per Algorithm 2 when the ERV does not necessarily

require immediate preemption and the TM utilizes this time to pro-

vide additional budget to the flows conflicting the ERV movement.

The budgets in this mechanism are assigned, such that the vehicle

queues in the ERV’s arterial and its links are maintained using Al-

gorithm 3. The vehicle queues are chosen based on the arrival time,

deadline and the delay tolerance of the ERV task. The arrival time

and the budget for the sporadic servers are set such that when the

servers are executed, the vehicle queues are dispatched just in time

to enable smooth and safe ERV traversal and thereby meeting the

local sub-job deadlines (hence the ERV deadline). Upon selecting

the proactive preemption, we calculate the number of traffic cycles,

𝑛𝑒𝑐 of𝑇𝑐 time in the time span of receiving the ERV information and

the deadline, 𝑑𝑒1of the first sub-job 𝑗𝑒

1(Line 3). Then, we find the

remaining time to 𝑗𝑒1’s deadline (Line 2). If the remaining time (𝑡𝑟 )

is less than the start-up lost time (𝑡𝑙 ) which represents the reaction

time to the green light for the first vehicle in the queue, then 𝑡𝑟 is

not enough to dispatch even one vehicle, and hence, a cycle time

(𝑇𝑐 ) worth of time is added to 𝑡𝑟 while subtracting one cycle from 𝑛𝑒𝑐(Line 5). This operation ensures that there is enough time for human

driven vehicles to react to green lights and incoming ERVs without

making hasty traffic decision and thereby reinforcing safety. We

then find the number of vehicles (𝑛𝑟 ) that we can dispatch within

𝑡𝑟 as well as the number of vehicles (𝑛𝑟𝑖𝑛 ) that enter the arterial

𝐴𝐷𝛼𝑒

at the worst-case (Line 6 and 7). This indicates that a queue

of 𝑞𝑒1= 𝑛𝑟𝑖𝑛 − 𝑛𝑟 in the first link can exist and still meet the first

sub-job’s deadline if we start ERV preemption at time 𝑛𝑒𝑐 . The queue

is also bounded by the link capacity to avoid spillbacks (Line 8).

Enabling green-wave coordination. : Since missing one of the sub-

job’s deadlines for the ERV task leads to a cascading effect for

all sub-jobs (Property 1), when the sub-job 𝑗𝑒𝑖is being executed,

the next link (corresponding to sub-job 𝑗𝑒𝑖+1) must be ready by

dispatching all vehicles within, before 𝑗𝑒𝑖reaches its deadline and

finishes execution. Since completion time for a sub-job 𝑗𝑒𝑖is equal

to the arrival time for the next sub-job 𝑗𝑒𝑖+1, the queues in each link

must be maintained (not exceeding the link capacity) such that the

links can be cleared (all vehicles dispatched) by the time the sub-job

ERV

Intersections

Figure 6: HIL framework with two intersections and an ERV

for the previous link completes execution (Line 10 and 11). This

ensures that by the time the previous sub-job reaches its deadline,

the next sub-job is ready for execution.

Budget assignment for proactive preemption. Consider that the ERVpreemption and traversal is requested in the arterial 𝐴𝐷

𝛼𝑒and using

Algorithm 3 we can determine the queues we need to maintain such

that all sub-jobs of the ERV task meet their deadline, the ERV task

hence meets its end-to-end deadline and green-wave coordination

is also enabled to ensure minimum stop-and-go traffic for higher

priority ERVs as well as the non-ERVs. Thus, the utilization bounds

for each server 𝑆𝐷𝛼𝑒 , 𝑖 = 1, . . . , _ within the arterial 𝐴𝐷𝛼𝑒

with queue

estimated as 𝑞𝑒𝑖can be formulated as,

𝑈𝐷𝑚𝑖𝑛𝛼𝑒

=ℎ · 𝑞𝑒

𝑖+ 𝑡𝑙

𝑇𝑐. (14)

The ERV-aware traffic control with proactive preemption is formu-

lated as follows.

maximize(Equation 4)

subject to𝑈𝐷𝑐𝛼𝑒 ≥ 𝑈

𝐷𝑐

𝑚𝑖𝑛𝛼𝑒(15)

𝑈𝐷′𝑐𝛼𝑒 ≤ 𝑈

𝐷′𝑐𝑚𝑎𝑥𝛼𝑒

(16)

Equations (7), (12), (13).𝐷𝑐 and 𝐷 ′𝑐 are conflicting pairs of traffic flows, as defined earlier.

Unlike critical preemption, in proactive preemption constraints in

Equations 15 and 16 enable dedicating some budget to the conflict-

ing flows as long as the minimum utilization demands of the servers

serving the ERV are satisfied, which ensures that the ERV deadlines

are met for each sub-job. Constraints in Equation 12 and 13 ensure

that the under-/over-utilization of resources for servers serving the

links not affected by the ERV is avoided and the schedulability of

the system (Equation 7) is maintained. Thus, by assigning sub-job

specific deadlines for the ERV task based on priority and delay

tolerance given by the triage scale, proactive preemption provides a

more planned approach towards the ERV traversal by avoiding long

queues and spillbacks before and during the ERV traversal. The

preemption mechanisms (critical and proactive) stay in effect until

the deadline of the corresponding sub-job has passed, i.e., until 𝑑𝑒𝑖.

In all, the critical preemption as well as the proactive preemption

provide strategies to enable ERV traversal such that their deadlines

are met and also control network-wide traffic to reduce queues

and traffic delays. Since ERV preemption still remains a priority

in both the preemption mechanisms discussed, there may be sce-

narios where long queues and potential spillbacks are unavoidable.

Specifically, we show in Section 6, that when there are heavy traffic

8

Timely and Non-Disruptive Response of Emergency Vehicles: A Real-Time Approach RTNS’2021, April 7–9, 2021, NANTES, France

Table 3: Flow types simulated as per the trafficflow rates andits description as per the FHWA [23]

.

Flow Type

Flow rate per lane

(Net flow in 3 × 3 network) Description

Low

1–4 veh/min

(540–2100 veh/hr)

Network running under capacity

with reduced travel delays

Medium

4–6 veh/min

(2100–3200 veh/hr)

Network nearing capacity

with longer queues

Heavy

up to 8 veh/min

(up to 4300 veh/hr)

Unstable traffic flow

with long wait times

flows in the network, enabling ERV traversal may lead to poten-

tial spillbacks. For such cases, we extend the per-arterial recoveryapproach presented in [26] to stabilize the entire network.

5.4.3 Scheduling in recovery phase. A recovery approach address-

ing a single arterial experiencing spillbacks was presented in [26].

Due to the lack of ERV preemption in their approach, their recovery

strategy fails to address cases when multiple arterials within the

network have long queues and potential spillbacks. Since multiple

conflicting flows experience prolonged red lights due to the preemp-

tion, especially when critical preemption is deployed, the recovery

approach must be extended for multiple links and arterials. We

therefore formulate a network-wide recovery approach as follows.

maximize (Equation 4)

subject to𝑈𝐷𝑐𝛼𝑒 = 𝑈

𝐷𝑐

𝑚𝑖𝑛𝛼𝑒(17)

𝑈𝐷′𝑐𝛼𝑒 = 1 −𝑈𝐷𝑐

𝑚𝑖𝑛𝛼𝑒(18)

Equations (7), (12), (13).In the recovery phase, we assign minimum budget requirement

to the servers that recently serviced the ERV (Equation 17) while

maximizing traffic flow for the conflicting servers (Equation 18).

Along with the constraint in Equation 13, the traffic through all

arterials conflicting the ERV flow will be maximized (Equation 4)

since assigned budget at𝑈𝐷𝑐𝛼 depends on𝑈

𝐷𝑐

𝛼−1. The recovery phaseis replaced with the default traffic strategy after one traffic cycle.

Table 1 refers to frequently used notations for the readers.

5.5 Worst-Case Performance Analysis forERV-Aware Traffic Control

We now provide a worst-case analysis to predict the impact of

the ERV traversal on the non-ERV flow which can help the traffic

routing systems to predict existing delays in the network. Worst-

case traffic delay accounts for the total time that a vehicle has to stop

while traversing through the network. Theorem 1 [26], presents a

worst-case traffic delay analysis without ERV traversal.

Theorem 1 ([24]). Assuming that the traffic flow rate for vehiclesentering the arterial 𝐴𝐷

𝛼𝑟, traveling through all links 𝐿𝑖 is 𝑎𝑖 , the

cumulative wait time𝑊𝐷𝛼𝑟,𝑝

for a vehicle at the 𝑝𝑡ℎ position in the

queue upon entering the arterial in the 𝑘𝑡ℎ cycle is bounded by

𝑊𝐷𝛼𝑟,𝑝 ∈

0,

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

©­«_𝑇𝑐 − _𝑈𝑚𝑖𝑛1,𝑘

𝑇𝑐 +_∑𝑖=2

(_ − 𝑖 + 1)𝑧𝑖ℎª®¬

(19)

where _ = 𝑛, if 𝐷 = {𝑆, 𝑁 }, and _ = 𝑚, otherwise. 𝑛𝑜𝑢𝑡1𝑘 is theminimum number of vehicles dispatched from link 𝐿1 of arterial 𝐴𝐷

𝛼𝑟

Table 4: ERV travel times in a 3 × 3 road networkPreemption

Strategy

ERV Travel Times (s)

Low Medium Heavy

No preemption 78 89 100

Localized 63 71 96

Green wave-based 60 60 60

Proactive preemption 60 60 60

in the 𝑘𝑡ℎ cycle, 𝑈𝑚𝑖𝑛1,𝑘denotes the minimum utilization demand

for link 𝐿1 in the arterial, in the 𝑘𝑡ℎ cycle, and all other variables areas defined previously.

We now present the cumulative worst-case non-ERV traffic delay

bounds caused by ERV traversal in Theorem 2.

Theorem 2. Assuming that an ERV traverses through the arterial𝐴𝐷𝛼𝑒

which conflicts the traffic flow within the arterial𝐴𝐷𝛼𝑒′ consisting

of links 𝐿𝑖 . Then the cumulative wait time𝑊 𝑒′𝛼𝑒′,𝑝 for a vehicle at the

𝑝𝑡ℎ position in the queue upon entering the arterial in the 𝑘𝑡ℎ cycleis bounded by

𝑊𝐷𝛼𝑒′,𝑝 ∈

[0,𝑊𝐷

_𝑖+𝑊𝐷

_𝑒+𝑊𝐷

𝑝𝑟𝑒𝑒𝑚𝑝𝑡 +𝑊𝐷_

](20)

where _ = 𝑛, if 𝐷 = {𝑆, 𝑁 }, and _ =𝑚, otherwise, and,

𝑊𝐷_𝑖

=

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

©­«_𝑖𝑇𝑐 − _𝑖𝑈𝑚𝑖𝑛1,𝑘𝑇𝑐 +

_𝑖∑𝑖=2

(_𝑖 − 𝑖 + 1)𝑧𝑖ℎª®¬ ,

𝑊𝐷_𝑒

=

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

(𝑑𝑒𝑒′−1 − 𝑎

𝑒𝑒′−1 − 𝑡𝑙

),

𝑊𝐷𝑝𝑟𝑒𝑒𝑚𝑝𝑡 = 𝑑𝑒𝑒′ − 𝑎

𝑒𝑒′ and

𝑊𝐷_

=

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

((_ − 𝑒)𝑇𝑐 − (_ − 𝑒)𝑈𝑚𝑖𝑛1,𝑘

𝑇𝑐 +_∑𝑖=𝑒

(_ − 𝑖 + 1)𝑧𝑖ℎ).

Proof:The arterials 𝐴𝐷

𝛼𝑒and 𝐴𝐷

𝛼𝑒′ will meet at the intersection 𝐼𝑒𝑒′ .

Consider that the ERV preemption is requested at 𝑡𝑑𝑖𝑠𝑝𝑎𝑡𝑐ℎ , when

the 𝑝𝑡ℎ vehicle has reached the intersection 𝐼_𝑖𝑒′ . Until the vehicle

reaches the intersection 𝐼_𝑖𝑒′ , its cumulative worst-case delay is

given by Theorem 1 [26] as,

𝑊𝐷_𝑖

=

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

©­«_𝑖𝑇𝑐 − _𝑖𝑈𝑚𝑖𝑛1,𝑘

𝑇𝑐 +_𝑖∑𝑖=2

(_𝑖 − 𝑖 + 1)𝑧𝑖ℎª®¬ , (21)

where, _𝑖 ∈ [1, 𝑒] and other notations are as before.

Let the local arrival time set by the TM task for the ERV to reach

the intersection 𝐼𝑒𝑒′ be given as, 𝑎𝑒𝑒′ . The vehicles traveling across

the arterial 𝐴𝐷𝛼𝑒′ can be described by two situations:

Case 1: The non-ERVs in 𝐴𝐷𝛼𝑒′ successfully cross the intersection 𝐼𝑒𝑒′

before𝑎𝑒𝑒′ (through proactive preemption). The budget,𝑈𝐷𝑐

𝛼′𝑒assigned

to the server serving the link 𝐿𝑒′ in the arterial 𝐴𝐷𝛼𝑒

is given by the

Equation 14. Therefore, the budget assigned to the server serving

the link 𝐿𝑒 in the arterial 𝐴𝐷𝛼𝑒′ is given as𝑈

𝐷′𝑐𝛼𝑒 = 1 −𝑈𝐷𝑐

𝛼′𝑒.

9

RTNS’2021, April 7–9, 2021, NANTES, France Oza et al.

Table 5: Effect of priority-based deadlines on overall trafficflow. 𝑐𝑒

𝑖and 𝑑𝑒

𝑖are the completion times and the deadlines

for the sub-job 𝑗𝑒𝑖of the ERV task arriving at 1100 s.

Priority

(𝜋𝑒 )𝑐𝑒1(s) 𝑑𝑒

1(s) 𝑐𝑒 (s) 𝑑𝑒

2(s) 𝑐𝑒

3(s)

𝑑𝑒3= 𝑑𝑒

(s)

Average Traffic

Delay (s)

1 1255 1255 1285 1285 1315 1315 39.97

2 1255 1274 1288 1296 1320 1330 36.75

3 1275 1285 1315 1315 1345 1345 35.45

4 1282 282 1315 1324 1350 1360 31.48

5 1307 1320 1345 1352 1383 1385 30.72

𝑳𝒊𝒋𝑬∗ (Link)

𝑰𝒊𝒊

𝑨𝜶𝒊𝑬 (Arterial)

𝑨𝜶𝒊𝑾

𝑨𝜶𝒊𝑺

𝑨𝜶𝒊𝑵

𝑳𝒊𝒋𝑺∗

𝑳𝒊𝒋𝑵∗

𝑳𝒊𝒋𝑾∗

(Servers)

Total Budget = 𝑻𝒄

Figure 7: A generic road network topology [26]

Therefore, the worst-case delay for the vehicle at the 𝑝𝑡ℎ position

is calculated from the Algorithm 3 and the Equation 14 as,

𝑊𝐷_𝑒

=

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

(𝑈𝐷𝑐𝛼′𝑒

𝑇𝑐

)⇒𝑊𝐷

_𝑒=

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

(𝑑𝑒𝑒′−1 − 𝑎

𝑒𝑒′−1 − 𝑡𝑙

)(22)

After crossing the intersection 𝐼𝑒𝑒′ , the vehicle will not be af-

fected by the ERV and the wait-time is given as (Theorem 1),

𝑊𝐷_

=

⌊𝑝

𝑛𝑜𝑢𝑡1𝑘

⌋∑𝑘=1

©­«(_ − 𝑒 )𝑇𝑐 − (_ − 𝑒 )𝑈𝑚𝑖𝑛1,𝑘

𝑇𝑐 +_∑𝑖=𝑒

(_ − 𝑖 + 1)𝑧𝑖ℎª®¬ , (23)

The worst-case delay under proactive preemption is given by,

𝑊𝐷𝛼𝑒′,𝑝 =𝑊𝐷

_𝑖+𝑊𝐷

_𝑒+𝑊𝐷

_.

The best-case occurs when the vehicles do not experience any

delays with green lights at each intersection before the ERV arrives.

The cumulative worst-case can thus be bounded by,

𝑊𝐷𝛼𝑒′,𝑝 ∈ [0,𝑊

𝐷_𝑖+𝑊𝐷

_𝑒+𝑊𝐷

_] . (24)

Case 2: The non-ERVs in 𝐴𝐷𝛼𝑒′ enter intersection 𝐼𝑒𝑒′ at 𝑎𝑒𝑒′ (critical

preemption). The maximum delay occurs if the 𝑝𝑡ℎ vehicle is un-

able to cross the intersection 𝐼𝑒𝑒′ before the ERV arrives at 𝑎𝑒𝑒′ . To

prioritize the ERV, the conflicting flows receive no budget until

𝑑𝑒𝑒′ , i.e., the deadline for the sub-job that corresponds to the ERV’s

traversal through the intersection 𝐼𝑒𝑒′ with the wait-time given by,

𝑊𝐷𝑝𝑟𝑒𝑒𝑚𝑝𝑡 = 𝑑𝑒𝑒′ − 𝑎

𝑒𝑒′, (25)

which adds to the wait-time determined in case 1. The cumulative

worst-case delay for this case is thus bounded by,

𝑊𝐷𝛼𝑒′,𝑝 ∈ [0,𝑊

𝐷_𝑖+𝑊𝐷

_𝑒+𝑊𝐷

𝑝𝑟𝑒𝑒𝑚𝑝𝑡 +𝑊𝐷_] .

5.6 Applicability to a Generalized TrafficEnvironment

For the ease of explanation, the system model (Section 3) assumes

a simplified road network and traffic constraints. Next, we describe

extending out approach to more a general traffic environment.

Varying road network topology and travel directions:While

the Manhattan grid-like road network with one-way travel restric-

tions (north-south or east-west) is commonly used to represent

tightly-spaced urban traffic setting, the proposed model can be ex-

tended to represent any large urban area with multiple links and

turning vehicles (Figure 7) by deploying additional servers [26].

Multiple servers can be grouped to serve non-conflicting traffic

flows such that the total budget (𝑇𝑐 ) is divided among all server

groups. The arrival rate information for the turning vehicles can be

obtained through strategically placed road-side units (RSUs) and/or

traffic pattern data [2]. For the road networks that do not follow

a grid-like topology, multiple closely spaced intersections can be

clustered under a purview of a single TM and multiple such TMs

can be deployed to cover the entirety of the road network [37]. Fur-

ther, Algorithm 1 shows that the deadlines are assigned to the ERV

at each intersection depending on the length of the link between

consecutive intersections. While the grid network provides the ease

of representation using an𝑚 × 𝑛 matrix, the proposed approach

can be deployed for varying lengths of links and arterials.

Estimating the worst-case traffic flow: Our approach requires

the traffic flow rates through the incoming entry points of the road

network under consideration to be known. To ensure worst-case

ERV delay guarantees, a constant, worst-case traffic flow rate is

used to calculate the deadlines for the ERV at each intersection.

Once the incoming flow rates from the edges of the network are

known, the traffic flow (ERV and non-ERV) through the links and

intersections in the interior of the network are controlled by the

budget assigned to each servers (as shown in Figure 7), and is thus

known. Similarly, while the worst-case delay analysis (Theorem 2)

assumes only straight-moving traffic, the worst-case performance

analysis can be extended for turning vehicle by considering the

appropriate servers along the path of the ERV (as discussed above).

Obtaining traffic data: In practice, the TM governing a network

experiencing heavy traffic (for example, downtown grids) are sur-

rounded by traffic signals that meter the flow through the denser

network [22] (in case of a standalone TM) or acquire the traffic

flow data from surrounding TMs (as a large urban area) through

connectivity among the RSUs [37]. Additionally, in dynamic condi-

tions, the worst-case traffic flow estimates (arrival rates and vehicle

queues) are utilized by the TM to calculate the signal timings only

for the next cycle and are updated at the start of every traffic cycle.

6 SIMULATIONS AND HARDWAREVALIDATION

We now present the large-scale traffic simulations and hardware-

in-loop (HIL) validation of our proposed approach.

6.1 Simulation SetupUsing a tick-based traffic simulator developed in Python 3, we sim-

ulate 1) vehicle flows varying from 60–600 veh/hr resembling the

critical volume-to-capacity ratios for signalized intersections [23]

10

Timely and Non-Disruptive Response of Emergency Vehicles: A Real-Time Approach RTNS’2021, April 7–9, 2021, NANTES, France

Table 6: Network-wide traffic delays under different ERV preemption approaches (shaded cells indicate spillbacks)Proposed Approach

Proactive Preemption + Recovery Proactive Preemption OnlyGreen Wave-based

Delay in

Conflicting

Flows (s)

Delay in

Conflicting

Flows (s)

Delay in

Conflicting

Flows (s)

ERV Arrival

Information

(s)

Traffic

Flow

Average Worst-Case

Average

Network-wide

Delays (s)

Average Worst-Case

Average

Network-wide

Delays (s)

Average Worst-Case

Average

Network-wide

Delays (s)

Low 68.65 77.12 37.56 70.54 75.53 38.23 89.06 90.12 39.56

Medium 71.23 81.12 40.12 76.34 82.12 42.12 104.21 119.31 42.4260

Heavy 88.64 92.12 46.42 93.23 103.12 47.21 100.21 112.21 49.21

Low 48.12 56.23 39.48 49.12 57.64 39.76 110.42 111.66 45.46

Medium 58.56 69.24 38.86 71.77 87.63 40.93 171.36 186.66 55.42120

Heavy 69.65 89.66 39.24 74.86 90.21 49.98 134.21 135.43 53.67

Low 47.83 56.11 35.85 59.06 68.92 38.42 93.23 103.10 44.88

Medium 42.07 53.12 35.29 54.48 65.61 38.26 107.85 113.44 44.64180

Heavy 52.16 64.76 34.59 61.41 67.30 38.22 167.83 169.62 61.24

as shown in Table 3, 2) desired 3 × 3 road network architecture

(Figure 1), and 3) different traffic algorithms, for one hour. An ERV

is introduced at around 1000 s. The length of each link and ERV’s

desired speed are set to 400m and 45mph respectively.

ERV travel times with different approaches: Table 4 shows

that our approach provides 15–37% faster ERV travel in medium and

heavy traffic, when compared to the localized preemption [5]. Our

approach also shows 40% faster ERV travel time when compared

to traffic control without ERV preemption [26]. Henceforth, since

localized preemption causes ERV travel delays, we only compare our

approach with the greedy green wave preemption [38] that always

provides best-case ERV travel times. We never see any difference inERV travel times with our approach and green wave approach.Effect of preemption and recovery on overall traffic delays(Table 6): When the ERV arrival information is received at 60,

120 and 180 s before its arrival, the proactive preemption with re-

covery shows 17.9%, 33.79% and 61.82% reduction in worst-case

traffic delays in conflicting flows, respectively, when compared to

the green wave approach. Therefore, the earlier the ERV informa-

tion is received, the better proactive decisions our approach makes.

Further, having a recovery phase after preemption improves the

performance by up to 21.48%, highlighting the need for an end-

to-end preemption. For all scenarios shown in Table 6, the ERV

requests highest priority and traverses the network without any

deadline misses. Our approach switches to critical preemption whenthe ERV information is received < 60 s of its arrival, and we still

see 8–26% improvement in traffic delays while avoiding spillbacks

when compared to the green wave-based approach.

Triage levels and its impact on network-wide traffic perfor-mance: Table 5 shows the completion time and the deadline for

the sub-jobs of the ERV task with the delay tolerance shown in

Table 2 for each priority level. Using priority information in traffic

planning and preemption could help achieve up to 23% improve-

ment in network-wide traffic delays between the highest and the

lowest priority ERV with 100% deadlines met for all priority levels.

ERV arrival information

ApproachingIntersection 1

ApproachingIntersection 2

Figure 8: ERV speeds with various preemption approaches

6.2 Hardware ValidationTraffic macro-simulations (Section 6) are employed to analyse large-

scale deterministic traffic parameters but rely on ideal properties

of vehicles and traffic flow [14]. Therefore, we also implement our

proposed approach on a hardware-in-loop (HIL) testbed consisting

of 30 small robots each representing a human-driven vehicle (Fig-

ure 6) to also validate our approach under non-ideal, more realistic

behavior. Our robots, affixed with infrared (IR) markers, are tracked

using the Optitrack motion capture system. The position data is

streamed to a Robot Operating System-based (ROS) [30] framework

that implements the traffic manager (TM) to control the traffic light

timings and vehicle flow. Two intersections of the 3 × 3 networkare physically mapped in the testbed, while the rest of the network

is simulated in software, due to limited physical space. We use the

intelligent driver model (IDM) [35] to mimic human driving in ur-

ban areas. The desired velocities are communicated to the robots

using Zigbee communication. One of the vehicles in the network is

labelled as an ERV which sends its information to the TM on the

ROS framework. The road architecture and vehicle dynamics are

scaled to the size of the robot. Interestingly, while our simulations

show no difference in ERV traversal times between our approach

and the green wave approach, our HIL experiment (Figure 8), that

considers non-ideal human reactions, shows our approach outper-

forms green wave preemption by ensuring non-stop ERV traversal

at the desired speed of 0.3 m/s.

7 CONCLUSION AND FUTUREWORKIn this paper, we represented ERV preemption and traffic flow

through a road network as a real-time scheduling problem. Us-

ing a deadline-driven approach, our proposed preemption strategy

provided guaranteed timely ERV response while also minimizing

traffic delays. Our approach shows up to 43% reduction in traffic

delays without adding any delay to the ERV travel, by proactively

controlling the traffic before, during and after the ERV traversal,

through the entire network. By leveraging the real-time properties

of our model, we provided worst-case wait time bounds for non-

emergency vehicles during ERV preemption which could further

help in planning predictable routes for the ERV dispatch systems.

Hardware-in-loop (HIL) experiments showed that with our pro-

posed approach, the ERV travels through the network without

deviating from its desired speed, thus adapting to urban driving

environment. Managing multiple ERV traversals through the road

network, and validating the proposed approach on a real road map

and traffic scenarios are left for future work.

11

RTNS’2021, April 7–9, 2021, NANTES, France Oza et al.

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